A274735
G.f. satisfies A(x) = (1 + x*A(x))^3 * (1 + x*A(x)^2).
Original entry on oeis.org
1, 4, 26, 210, 1901, 18445, 187524, 1971672, 21263360, 233907762, 2614446624, 29607343948, 338977591904, 3917185497535, 45629006313280, 535199773167207, 6315789123860388, 74932400322972992, 893276792585933870, 10694510040508714014, 128531711285410216883, 1550159476645634696615, 18755239991772817629972, 227577929298568261967650, 2768820313297861609739979
Offset: 0
G.f.: A(x) = 1 + 4*x + 26*x^2 + 210*x^3 + 1901*x^4 + 18445*x^5 + 187524*x^6 + 1971672*x^7 + 21263360*x^8 +...
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{a(n) = my(A=1); for(i=1,n, A = (1 + x*A)^3 * (1 + x*A^2) + x*O(x^n) ); polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
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{a(n) = my(A=1); A = (1/x)*serreverse(x*(1-x*(1+x)^3)/(1+x +x^2*O(x^n) )^3 ); polcoeff(A,n)}
for(n=0,30,print1(a(n),", "))
A274379
G.f. satisfies A(x) = (1 + x*A(x))^3 * (1 + x^2*A(x)^3).
Original entry on oeis.org
1, 3, 13, 70, 429, 2842, 19794, 142758, 1056655, 7980280, 61251261, 476387379, 3746317414, 29738316330, 237968639936, 1917578268288, 15546796822656, 126728260011920, 1037987924978125, 8538459191677170, 70509828893263474, 584310452973463242, 4857624566855734836, 40501472981905806550, 338594135314564168494, 2837641019938074131463, 23835438376045780734390, 200633658871150345742269, 1692132786239339256115050, 14297391426538004065333910, 121009206594941545408186768
Offset: 0
G.f.: A(x) = 1 + 3*x + 13*x^2 + 70*x^3 + 429*x^4 + 2842*x^5 + 19794*x^6 + 142758*x^7 + 1056655*x^8 + 7980280*x^9 + ...
such that A(x) = 1 + 3*x*A(x) + x^2*(3*A(x)^2 + A(x)^3) + x^3*(A(x)^3 + 3*A(x)^4) + 3*x^4*A(x)^5 + x^5*A(x)^6.
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{a(n) = my(A=1); for(i=1, n, A = (1 + x*A)^3 * (1 + x^2*A^3) + x*O(x^n) ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
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{a(n) = my(A=1); A = (1/x)*serreverse(x*(1-x^2*(1+x)^3)/(1+x +x^2*O(x^n) )^3 ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
A369623
Expansion of (1/x) * Series_Reversion( x / (1/(1-x)^3 + x^3) ).
Original entry on oeis.org
1, 3, 15, 92, 624, 4509, 34033, 265164, 2116560, 17219068, 142252608, 1190173956, 10064038469, 85873044573, 738446318232, 6393218956733, 55680130965252, 487488352916496, 4288083926110045, 37878037865662422, 335859658273133355, 2988274511990407436
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)^3+x^3))/x)
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a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(4*n-6*k+2, n-3*k))/(n+1);
A369599
Expansion of (1/x) * Series_Reversion( x * (1/(1+x)^2 - x^3) ).
Original entry on oeis.org
1, 2, 5, 15, 54, 223, 993, 4580, 21521, 102563, 495318, 2422302, 11979965, 59824535, 301202673, 1527118720, 7789673832, 39947163395, 205835776301, 1065155017623, 5533253267649, 28844759080896, 150846487065730, 791163319140664, 4160593763997122
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x)^2-x^3))/x)
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a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(2*n+2*k+2, n-3*k))/(n+1);
Showing 1-4 of 4 results.
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